Parallel algorithm for computing fixpoints of Galois connections

Abstract

This paper presents a parallel algorithm for computing fixpoints of Galois connections induced by object-attribute relational data. The algorithm results as a parallelization of CbO (Kuznetsov 1999) in which we process disjoint sets of fixpoints simultaneously. One of the distinctive features of the algorithm compared to other parallel algorithms is that it avoids synchronization which has positive impacts on its speed and implementation. We describe the parallel algorithm, prove its correctness, and analyze its asymptotic complexity. Furthermore, we focus on implementation issues, scalability of the algorithm, and provide an evaluation of its efficiency on various data sets.

Keywords

Galois connection Fixpoint Formal concept Parallel algorithm

Supported by research plan MSM 6198959214. Partly supported by grant P103/10/1056 of the Czech Science Foundation.